Proof step e-13c78408b476aecd

basis_map A007318 → concludes about basis_map_A007318 of Triangle of coefficients in expansion of (1+4x)^n. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A007318",
  "operation": "basis_map"
}

Premises

• Triangle of coefficients in expansion of (1+4x)^n. (sequence)
  uses: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]

Claims

• { "claim": "real_rooted", "from_index": 0, "region": { "upper": { "closed": true, "value": "0" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 c4e5dfee164f1be46b32d25aae8fa7864973f463379c921dcf1a7f12fd095ea8, 6,855 bytes (1,385 compressed); download JSON

Cited by

• n-d04994959b21388c (real_rooted)
• n-d04994959b21388c (one_signed_coefficients)
• n-d04994959b21388c (hadamard_kernel)